Answer:
[tex]P\left(8\right)=0[/tex]
Step-by-step explanation:
Assuming that a fair die is rolled.
Let X be the set of all possible outcomes. Let A be an outcome.
So, the probability that A occurs is:
[tex]P\left(A\right)=\frac{|A|}{|X|}[/tex]
As the set of all possible outcomes of the roll of a single die is:
[tex]X=\left\{1,2,3,4,5,6\right\}[/tex]
Observe that
[tex]|X|=6[/tex]
Here
[tex]|A|=0[/tex] because 8 is not in the set sample space. So, the outcome of occurring the number 8 is not possible from the all possible outcomes.
So, the probability must be zero.
In other words,
[tex]P\left(A\right)=\frac{|A|}{|X|}[/tex]
[tex]P\left(8\right)=\frac{0}{6}=0[/tex]
Therefore,
[tex]P\left(8\right)=0[/tex]
The value of P(8) is 0.
Given
Assume that a fair die is rolled.
The sample space is, 1, 2, 3, 4, 5, 6, and all the outcomes are equally likely.
A sample space is a collection of a set of possible outcomes of a random experiment.
Let X be the set of all possible outcomes and A be an outcome.
Then,
The probability of A occurs is;
[tex]\rm P(A)=\dfrac{|A|}{|X|}[/tex]
Total number of sets X = 6
And 8 is not in sample space so A = 0
Substitute all the values in the formula;
[tex]\rm P(A)=\dfrac{|A|}{|X|}\\\\\rm P(8)=\dfrac{|0|}{|6|}\\\\P(8)=0[/tex]
Hence, the value of P(8) is 0.
To know more about sample space click the link given below.
https://brainly.com/question/15659544
